WASHINGTON—President Barack Obama is expected to order a rule change this week that would require employers to pay overtime to a larger number of salaried workers, two people familiar with the matter said.

Currently, many businesses aren't required to pay overtime to certain salaried workers if they earn more than $455 a week, a level that was set in 2004 and comes to roughly $24,000 a year. The White House is expected to direct the...